Self-aggregation of cationic gemini surfactants with amide groups in the spacer and variable alkyl chain length

Synthesis, aggregation parameters and antimicrobial activity of novel cationic gemini surfactants with two amide groups in gemini spacer structure and a variable number of carbon atoms in alkyl tails ranging from 12 to 15 are reported. The critical micelle concentration of gemini surfactants was determined using surface tension and electrical conductivity methods. The cmc values were found in the range 0.83 to 0.06 mM. The interfacial area, micelle ionisation degree and the Gibbs free energy per molecule and alkyl chain were calculated from the surface tension and conductivity curves. Particle size analysis using the dynamic light scattering method confirmed the formation of small spherical micelles 6–7 nm large in size for gemini surfactants with 12 and 13 carbon atoms in the alkyl chain. A large size above 50 nm was found for the aggregates composed of long-chain gemini molecules with 14 and 15 carbon atoms. The zeta potential of gemini surfactants shows a continuous increase with the increasing alkyl chain length. Micelle aggregation number of gemini surfactants correlates well with the hydrodynamic size data. Small aggregation number values were found for short-chain gemini molecules with 12 and 13 carbon atoms in the alkyl chain. Long-chain gemini molecules with 14 and 15 carbon atoms exhibit aggregate growth represented by an increase in the aggregation number values while maintaining the spherical or spheroidal shape of micelles. The investigations of antimicrobial activity against Gram-positive bacteria, Gram-negative bacteria and yeast indicate the increasing antimicrobial efficiency towards the short-chain surfactant with 12 carbon atoms in the alkyl chain. A possible cut-off effect presence is proposed to explain the dependence of antimicrobial activity on the surfactant alkyl tail length.


Introduction
Gemini surfactants continue to attract a lot of interest from both academia and industry over the past decades.Anionic gemini surfactants exhibit good dispersing ability and can be produced at low cost which enables them for use as laundry detergents, in enhanced oil recovery and emulsification processes [1][2][3].Due to their pH-sensitiveness, low skin and eye irritation, outstanding water solubility, high degree of biodegradation and low critical micelle concentration, zwitterionic gemini surfactants are promising systems for a wide range of applications such as pharmacy, cosmetics, textile industry, leather finishing, novel materials production, etc. [4][5][6].The major group of gemini surfactants focused on a variety of applications are cationic gemini surfactants [7,8].They cover a broad field of applications ranging from enhanced oil recovery [9,10], moisteners of coal pitch [11] and lignite [12], corrosion inhibitors [13][14][15][16][17][18][19][20] up to modern applications in nanosystems such as dispersion of nanotubes [21] and stabilisation of gold and silver nanoparticles [22][23][24][25][26][27].
The presence of weak amide or ester group in surfactant molecular structure provides these molecules with new features that turn them into environmentally friendly systems."Soft" surfactants containing amide or ester group are decomposed into structurally simpler products more easily than their "hard" hydrocarbon analogues.In vitro enzymatic hydrolysis of the ester bond in "soft " cationic surfactants with variable alkyl chain length showed the dependence of the hydrolysis rate on the alkyl chain length [28].The presence of an amide group in single-chain cationic surfactant N-anilinoformylmethyl-N-cetyl-N,N-dimethylammonium chloride improves surfactant adsorption when compared to the conventional benzylcetyldimethylammonium chloride [29].The amide bond in a single-chain surfactant structure is reported to substantially increase the hydrophilicity of the amphiphile through its ability to form intermolecular hydrogen bonds that lead to a tighter packing at the air-water interface or hydrophobic surface [30].Synthesis and investigations of aggregation properties of gemini surfactants with amide or ester group located in the spacer of a gemini molecule [31][32][33][34][35][36][37], or as a part of the alkyl tails [34,[38][39][40] are reported as well.Some of the aggregation parameters of gemini surfactants such as the micelle aggregation number are directly affected by the number and position of amide groups in the gemini surfactant structure [40].The studies indicate that the location of the ester or amide group in the spacer of a gemini molecule is more favourable for biodegradation than the location in alkyl tails [41].On the other hand, the location of ester groups in hydrophobic alkyl tails decreases the solubilising power of gemini surfactants [42].Biodegradable cationic gemini surfactants are reported to show potent biological properties such as cytotoxicity and antimicrobial activity [43].
Usually, aggregation properties of cationic gemini surfactants are studied as a function of the molecular structure and the length of the gemini surfactant spacer [44][45][46][47][48][49][50].To the best of our knowledge, a significantly smaller number of works are oriented on the investigation of the self-assembly of cationic gemini surfactants as a function of the alkyl chain length [51][52][53].Aggregation parameters of cationic gemini surfactants with diester and diamide spacers were studied as a function of the spacer length in our previous study [37].The present work aims to extend these investigations towards cationic bisammonium gemini surfactants with a variable alkyl chain length in the search for a gemini molecule with biodegradable properties for a variety of applications such as synthesis and electrostatic stabilisation of metal nanoparticles [23,27].

Synthesis of bisammonium surfactants
AM (0.05 mol) was added to a solution of 1-bromoalkane (0.11 mol) and acetonitrile (30 mL).The reaction mixture was refluxed at 100 °C for 4 h.After cooling down the mixture to room temperature, the solvent was evaporated under reduced pressure and the product was crystallised from methanol.The bisammonium surfactants AM12, AM13, AM14 and AM15 were obtained in yields 73%, 70%, 83% and 85%, respectively.All chemicals used in the synthesis (p.a.grade) were purchased from commercial suppliers.The chemical identity of synthesised surfactants was confirmed by 1 H-and 13 C-NMR spectra measured on a Mercury plus spectrometer in CD 3 OD.The chemical shifts were referenced with respect to an internal TMS signal.NMR recordings for individual surfactants are shown below.

Electrical conductivity
The electrical conductivity of gemini surfactant solutions was measured at 25 °C using a WTW Tetracon 325 electric conductivity bridge.Gemini surfactants cmc was determined in the automated measurement cycle where specific volumes of stock surfactant aqueous solution were added to the 20 mL of solvent using a computer-controlled 765 Dosimat (Metrohm) dispensing unit based on the precalculated list of surfactant concentrations.A custom-written software controlled the dosing process and provided the real-time collection and storage of conductivity data from the conductivity bridge.The cmc of gemini surfactants AM(m), m = 12 -15, was calculated as the intersection of two linear regions in the conductivity vs. surfactant concentration dependence using the linear regression method with the respective errors for the fitting constants.Micelle ionisation degree α was calculated as the ratio of the slopes of the linear regions above and below the cmc [54].The Gibbs free energy of micellisation, ΔG mic per molecule of a gemini dicationic surfactant, is calculated from the cmc and micelle ionisation degree α utilising the following equation [48]: α is the micelle ionisation degree, T is the absolute temperature, and R is the gas constant.The constant 55.5 is the number of moles in 1 L of solvent (water).When assuming ΔG mic per single alkyl chain of a gemini dicationic molecule, Formula (1) can be rewritten as follows [55]:

Surface tension
The surface tension of surfactant solutions was measured by using a computer-controlled Krüss K100MK2 tensiometer with the Wilhelmy plate method.The data were recorded after the surface tension equilibrium value had been reached (usually 30-150 min from the start of the measurement).The measurements were carried out at 25 °C.The surface excess Π is related to the experimentally determined slope of the surface tension vs. log surfactant concentration dependence in the premicellar region (dγ/dlog c) p,T using the Gibbs adsorption equation [56]: Π is expressed in mol/1000m 2 , (dγ/dlog c) p,T is expressed in mN/m, R = 8.31 J K −1 mol −1 and T = 298.15K.The value of the prefactor i = 3 which applies to ionic gemini surfactants was used in Eq. (1).The area per surfactant molecule A in nm 2 is calculated from the surface excess Π as follows [56]: where N A is the Avogadro's number.

Dynamic light scattering
A Brookhaven light scattering system BI 9000, goniometer SM200, and an argon laser (the applied wavelength 514.5 nm) were used for the dynamic light scattering measurements.The scattered intensity was registered at 90° and the temperature of 25 °C.From the time correlation function, the translation diffusion coefficient was calculated using the method of cumulants.The method of cumulants was used for the calculation of the mean particle diameter from the expansion of the logarithm of the time correlation function into a series up to the second quadratic term.The diffusion coefficient was determined from the correlation function decay rate and the hydrodynamic diameter was calculated from the diffusion coefficient using the Stokes-Einstein formula.The mean value and the standard deviation of the hydrodynamic diameter were calculated for each AM(m) surfactant.Particle size spectra of AM(m) surfactants were calculated from the particle size distributions which resulted from the application of the constrained regularised algorithm CONTIN [57] on the time correlation function.Surfactant solutions for the light scattering measurements were prepared using deionised water and filtered for mechanical impurities through syringe filters with the 0.45-µm pore size.For each surfactant, 5 independent measurements of the time correlation function were recorded at the surfactant concentration 10 × cmc.After the elimination of measurements with large experimental error, the mean value and the standard deviation of micelle hydrodynamic size using the cumulants method were calculated.

Zeta potential
A Brookhaven BI ZetaPlus meter was used for the zeta potential determination.Zeta potential values were calculated from the measured electrophoretic mobility using the Smoluchowski limit for the mobility vs. zeta potential relationship.The mean value was calculated from a statistical set of 20 zeta potential recordings per surfactant concentration.The measurements were taken at 25 °C.

Time-resolved fluorescence quenching
The fluorescence decay curves were recorded using a lifetime fluorescence spectrometer LifeSpec II (Edinburgh Instruments) and F900 control software.The spectrometer was operating at a 381-nm emission wavelength and the decay curves were fitted to Eq. ( 5) [58]: with the nonlinear least squares procedure using the Origin 2022b software package.I(t) and I(0) are the fluorescence intensities at time t and zero time, respectively.τ 0 , τ Q and R are the nonlinear fitting parameters where k Q = 1/τ Q is the rate constant for a fluorescence agent quenched by a quencher in a micellar solution.The micelle aggregation number N is related to the fitting constant R and the concentration of surfactant and quencher as follows [58]: c Q is the quencher concentration and c surf is the surfactant molar concentration.
In the fluorescence quenching experiments, pyrene was used as a fluorescence agent and cetylpyridinium chloride as a quencher.The pyrene concentration was kept at a low level so that the ratio of pyrene concentration/concentration of surfactant micelles in the solution was < 0.05.The concentration ratio quencher concentration/concentration of surfactant micelles was close to 1 so the quencher distribution is approximately one quencher molecule per micelle.The surfactant concentrations used were high enough to ensure that pyrene and quencher were completely solubilised in the micelles.The micelle aggregation number was determined at the surfactant concentration in the range 4-30 × cmc.All measurements were performed at 25 °C.

Antimicrobial activity
The antimicrobial activity of the series of AM(m) gemini surfactants was evaluated in vitro and expressed as the minimum inhibitory concentration (MIC).It was determined using the standard broth dilution method [59].The following strains of Gram-positive bacteria, Gram-negative bacteria and a yeast pathogen were selected for the experiments: Staphylococcus aureus CNCTC Mau 29/58, Escherichia coli CNCTC 377/79 and Candida albicans CCM 8186, respectively.The tested bacterial strains were purchased from the Czech National Collection of Type Cultures (Prague, Czech Republic); yeast was obtained from the Czech Collection of Microorganisms (Brno, Czech Republic).

Aggregation and surface properties
The main aggregation parameter, the cmc of AM(m) surfactants, was determined using the two experimental methods-surface tension and electrical conductivity.The tensiometry data provide the dependencies of surface tension on log surfactant concentration which show two linear parts with the intersection indicating the cmc values of AM(m) gemini surfactants (Fig. 1).The cmc was found to be in the decimal order range 10 −4 to 10 −5 M for the interval of alkyl chain length ranging from 12 to 15 carbon atoms.The fitting lines shown in Fig. 1 were obtained using linear regression.The cmc values were calculated as the concentration at the intercept of the lines in premicellar and micellar regions using the regression fitting parameters.The cmc data determined in tensiometry experiments are denoted as cmc γ as shown in Table 1 with the standard error values.
The slopes in the premicellar region in Fig. 1 were used for the calculation of surface excess Π according to the Gibbs adsorption in Eq. ( 3) and for the determination of area per gemini molecule at the air/water interface A (Eq. ( 4)).The plots of electrical conductivity vs. surfactant concentration (Fig. 2) show a linear conductivity increase in the premicellar and micellar regions of surfactant concentration with different slopes in each region.
Analogous to the cmc calculation from the tensiometry data, the cmc values were calculated as the concentration at the intercept of two linear parts in these regions.The cmc data from conductivity measurements denoted as cmc σ are shown in Table 1.The ratio of the slopes in the premicellar and micellar regions gives the micelle ionisation degree α that is shown in Table 1 for all investigated gemini surfactants.Using α, the Gibbs free energy of micellisation per molecule and alkyl chain, ΔG molecule (Eq.( 1)) and ΔG chain (Eq.( 2)) respectively, are calculated and presented in Table 1.
According to the data shown in Table 1 and Fig. 3a, cmc γ and cmc σ values were found to be in the range 0.83 to 0.06 mM showing decreasing tendency with the increasing alkyl chain length from 12 to 15 carbon atoms.Figure 3a shows a linear decrease of log cmc on the alkyl carbon number m for both experimental methods which confirms the constant amount of Gibbs free energy necessary for the transfer of a gemini molecule from the interface into the micellar phase when the alkyl chain is extended by single CH 2 group.A somewhat smaller cmc γ , when compared to conductivity values of the cmc, is related to the used tensiometry technique which is more sensitive to the subtle changes in the air-water interface saturation by gemini molecules than the micellisation in the solution bulk.In  the latter case, a detectable change in the number of free counterions providing the conductivity of surfactant solution requires a significant number of formed micelles which shifts the cmc to higher values.
A few studies on the aggregation of gemini surfactants report a similar range of cmc values for a comparable interval of alkyl chain length of surfactant molecules.In the study [60], cmc values are reported to be 0.98 mM and 0.02 mM for gemini surfactants 1,4-hexamethylene-bis(N-alkyl-N,Ndimethylammonium bromides) with the alkyl chain length 12 and 18 carbon atoms, respectively.Bisammonium gemini surfactants with ether-based spacer, 3-oxa-1,5-pentanebis(N-alkyl-N,N-dimethylammonium bromides), were found to have cmc values in the range 1.05-0.03mM for alkyl chain length from 12 to 16 carbon atoms [61].These reported cmc values are slightly higher than our cmc values listed in Table 1, especially for the short alkyl chain members of the investigated surfactants series.This may be related to the presence of two amide groups in the spacer of AM(m) gemini surfactants.A similar observation has been made based on the small-angle neutron scattering study of gemini surfactants with amide groups in the spacer, where the amide functionality was found to enhance the surfactant aggregation properties as compared to the surfactants having no amide bond in their structure [40].The plot of surface tension vs log surfactant concentration shows two breakpoints for the surfactant AM15 with the longest alkyl chain (Fig. 1) indicating possible premicellar aggregation.This aberrant aggregation behaviour of long-chain surfactants has been reported for cationic gemini surfactants with a phenyl group in the spacer and 18 carbon atoms in the alkyl chain [62].Aqueous solutions of this gemini surfactant display unusual surface properties, showing two breakpoints in the surface tension curve.Whereas the micellisation process and the cmc are assigned to the breakpoint at higher surfactant concentration, the first breakpoint is interpreted in terms of oligomers composed of several surfactant molecules that begin to grow rapidly until finally reaching the point when no further surface tension decrease is observed and true micelles are formed [62].This may be also the case of AM15 surfactant where the second breakpoint indicated by the arrow (Fig. 1) is related to the cmc.Two breakpoints do not appear in the conductivity vs. concentration dependence of AM15 (Fig. 2), possibly due to the smaller sensitivity of the conductivity method at low surfactant concentration.The subtle changes in the free counterions concentration reflecting the formation of premicellar aggregates may lie below the detection limit of the conductivity method.As the data in Table 1 indicate, both cmc and γ cmc decrease with increasing m due to the increasing hydrophobic effect because of the alkyl chain extension.The dependence of interfacial area A on m is weak, showing a decrease for the surfactant with the longest alkyl chain AM15 (Fig. 3b, Table 1).This interfacial area decrease at m = 15 corresponds with the increased level of hydrophobic interaction between long alkyl chains, as documented by the occurrence of possible pre-aggregation effects in the surface tension plot (Fig. 1).A similar drop in the interfacial area is reported for the long alkyl chain homologs of the series of anionic carboxylate gemini surfactants with amide groups [63].On the other hand, the smaller interfacial area value for the short-chain homolog AM12 is somewhat surprising.Irregularities in the interfacial area dependence on the alkyl chain length are also observed in the previously cited reference at the short end of the surfactant series with variable alkyl chain length, between 10 and 14 carbon atoms [63].Of this series, the anionic gemini surfactant member with 10 carbon atoms shows an unexpectedly small interfacial area value.We can assume that shorter alkyl chains result in an insufficient hydrophobic interaction with fluctuations present in the arrangement of alkyl chains in the surfactant hydrophobic layer which may be responsible for the irregularities in the interfacial area values.These conformational fluctuations may be also related to the possible cis/trans conformational change of alkyl chain arrangement in a gemini molecule which is observed for bisammonium gemini surfactants if their polymethylene spacer is sufficiently short (2-3 CH 2 groups) [44].This small number of carbon atoms in the spacer is identical to that in the central polymethylene part between two amide groups in the spacer of our series of AM(m) gemini surfactants.The plot in Fig. 3c shows the dependence of the micelle ionisation degree α on the carbon atom number m.The dependence of α on the gemini molecular structure correlates with the aggregate shape curvature, the changes of which are reflected in the degree of binding of counterions to the micelle surface and, hence, in the value of α. α is indirectly controlled also by the arrangement of hydrophobic parts of a gemini molecule, mainly by their stiffness or flexibility.These parameters are related to the chemical composition, the presence of substituents and the length of hydrophobic parts of gemini molecules.Therefore, the dependence of α on these factors is complex.As the reported α values for various gemini structures indicate, the dependence of α on the spacer length of gemini molecule was found to be increasing in the case of bisammonium gemini surfactants with polymethylene spacer [44] or gemini surfactants with polymethylene spacer and ethyl ammonium headgroups [64] which is to relate to the stiffness and rigidity of a stretched polymethylene spacer.On the other hand, the elongation of the alkyl substituent on the amine group in the central position of polymethylene spacer from 2 to 8 carbon atoms does not significantly change the α values [65].In our case, α values indicate the increasing trend with the increasing m values, especially for long-chain homologs AM14 and AM15.According to Fig. 3c and Table 1, the α values of AM12 and AM13 are 0.29 and 0.34, respectively, while α of AM14 and AM15 is close to 0.50.
The Gibbs free energy values per molecule ΔG molecule and alkyl chain ΔG chain show a weak dependence on the carbon atom number m, providing the values − 67 to − 65 kJ/mol and − 35 to − 33 kJ/mol for ΔG molecule and ΔG chain , respectively (Fig. 3d).This indicates a spontaneous micellisation effect for all studied homologs of the investigated surfactant series.

Hydrodynamic size and zeta potential
The mean hydrodynamic size of AM(m) surfactants was determined using dynamic light scattering measurements according to the procedure described in the "Methods" section.A set of screenshots with the calculations of translational diffusion coefficient, hydrodynamic diameter and polydispersity as well as the particle size distributions are shown in the Supplementary information file for each surfactant AM(m).In Fig. 4a, the micelle hydrodynamic diameter of gemini surfactants is shown as a function of m.
The data in Fig. 4a indicate that AM12 and AM13 form small spherical micelles with a mean size between 6 and 7 nm even.We observed similar values of micelle size in our previous study focused on the differences in aggregation properties between diamide and diester bisammonium gemini surfactants.The bisammonium gemini surfactants with two dodecyl chains, two amide groups in the spacer and a variable number "s" of CH 2 groups in the central polymethylene part of the spacer form spherical micelles with the size between 3 and 11 nm (s = 2 -8).This indicates that two dodecyl chains in a diamide gemini molecule, even with the longest central part of the spacer with 8 carbon atoms, are too short to provoke a strong hydrophobic interaction that would result in the formation of more complex aggregates like long rodlike micelles or vesicles.The extension of alkyl chains results in an increase in hydrodynamic diameter.The members of the series with a longer alkyl chain AM14 and AM15 have a mean aggregate size of 137 nm and 169 nm, respectively, as determined by the cumulants method (Fig. 4a).The particle size spectra of AM(m) gemini surfactants calculated by the CONTIN algorithm from the time correlation function confirmed the presence of small spherical micelles of AM12 and AM13 with a diameter of approximately 3 nm, while the size of AM14 and AM15 micelles increased to 151 nm and 170 nm, respectively (Fig. 5).
A larger size of the aggregates composed of AM14 and AM15 gemini molecules in the particle size spectra (Fig. 5) as well as the plot of their mean diameter (Fig. 4a) may evoke a question about the shape of the formed micelles.To analyse the shape of AM14 and AM15 micelles, we measured the angular dependence of the scattered light from micellar solutions of both gemini surfactants at the concentration 10 × cmc.The angular dependence of the scattered light allows to determine the radius of gyration R g of surfactant aggregates and to calculate the ratio R g /R h (R h -hydrodynamic radius) which reflects the geometry and the shape of surfactant aggregates.As the measurements and calculations indicate, the ratio R g /R h is equal to 1.08 and 0.84 for AM14 and AM15 micelles, respectively, which is close to the value 0.78 for spherical aggregates.We assume that both surfactants form spherical or spheroidal aggregates at the investigated concentration.The measurement procedure and references, related mathematical equations and the data analysis are shown in the Supplementary information file.
The zeta potential of AM(m) gemini surfactants shows an increase with m, from + 35 mV for AM12 up to + 83 mV for AM15 (Fig. 4b).The data sets for each AM(m) surfactants are shown in the Supplementary information file.To reach a minimum electrical conductivity value necessary for the proper mobility and zeta potential calculation, the measurements were carried out in the interval of surfactant concentrations-AM12: 30 × cmc, AM13: 50 × cmc, AM14: 10 × cmc, AM15: 10 × cmc.The plot insets in Fig. 4b show examples of zeta peaks for individual gemini surfactants.Zeta potential gradually increases with the increasing m which, to a certain extent, correlates with the hydrodynamic size increase depicted in Fig. 4a.Our previous study of bisammonium gemini surfactants with two amide groups in the spacer, dodecyl chains and a variable spacer length revealed a weaker dependence of zeta potential values on the spacer length [37].Zeta values were found to be in the range between + 16 and + 42 mV, and micelles composed of gemini molecules with the longest central spacer part (8 CH 2 groups) had zeta values barely exceeding + 35 mV which is the value for AM12 [37].The extension of the central hydrophobic spacer part does not result in the dramatic change of aggregation parameters such as aggregate size and zeta potential.Polymethylene spacers with this length of 8 CH 2 groups of gemini molecules with dodecyl chains are known to be rigid and displaced at the air-water interface while not bending into the hydrophobic phase [45].As a result, only spherical micelles are formed of these gemini molecules [66] with no significant aggregate growth.On the other hand, the extension of two alkyl chains in AM(m) to 14 and 15 carbon atom molecules seems to sufficiently increase the level of hydrophobic interaction between neighbouring molecules which is reflected in the interfacial area decrease and aggregate growth.

Micelle aggregation number
The dependence of micelle aggregation number N of AM(m) gemini surfactants as a function of surfactant concentration relative to the cmc is shown in Fig. 6a, as determined by the time-resolved fluorescence quenching method.The dependence of N on the alkyl chain number m at the constant surfactant concentration 10 × cmc is shown in Fig. 6b.
The fitting constant R from the fluorescence decay measurements (Eq.( 5) of the experimental section) and the aggregation number N of AM(m) micelles as a function of surfactant concentration and the spacer length are listed in Table 2.
N almost does not depend on gemini surfactant concentration (Fig. 6a) for all investigated alkyl chain lengths of AM(m) surfactants.This corresponds with the frequent experimental observation of a weak dependence of the hydrodynamic size and the aggregation number of surfactant micelles in diluted solutions.A strong dependence of these aggregation parameters on the surfactant alkyl chain length m is observed.The light scattering data (Figs.4a and 5) indicate an increase in apparent hydrodynamic size, especially for long-chain homologs AM14 and AM15.This trend is obvious from the fluorescence quenching experiments, as well.At the constant surfactant concentration 10 × cmc (Fig. 6b), an increase in aggregation number with the increasing alkyl chain number m is observed.The first two data points (AM12 and AM13) represent small micelle aggregation numbers 27 and 29, respectively (Table 3), while an increase in N is observed for AM14 (N = 53) and, more clearly, for AM15 (N greater than 200).The aggregation number values for AM12 and AM13 correlate well with the small hydrodynamic diameter of AM12 and AM13 aggregates and indicate the formation of small spherical micelles.For AM14 gemini molecules, the hydrodynamic size above 100 nm and the micelle aggregation number around 50 indicate that AM14 micelles remain still spherical.A similar case of spherical or spheroidal micelles is reported for cationic bis(dodecyldimethyl)ammonium bromide gemini surfactants with a polymethylene spacer of variable length (3-12 CH 2 groups) with higher aggregation numbers varying between 25 and 100 [66].A more pronounced increase in the aggregation number is observed for  AM15 with the longest alkyl chains of the investigated surfactant series.Figure 7 shows the fluorescence decay curves used for the aggregation number calculation.The slope of the initial decrease of fluorescence intensity (close to zero decay time) is changed for AM14 and more clearly for AM15.A steeper decrease of AM14 and AM15 curves at zero decay time results in the increase of the fitting constant R (Table 3) and, consequently, of the aggregation number.As the study on the determination of the aggregation number of single-chain surfactants indicates, surfactant micelles grow slowly, while maintaining a more or less spherical shape up to the aggregation number of 110-130 [67].Despite higher aggregation number values of AM14 and AM15 surfactants, we assume that their micelles maintain spherical or spheroidal shape, as demonstrated by the determination of the ratio R g /R h in the dynamic light scattering section.

Antimicrobial activity
The bar graph in Fig. 8 shows the logarithm of the inverse minimum inhibitory concentration (MIC) plotted as a function of the number of carbon atoms m of AM(m) gemini surfactants.The activity was determined against Gram-positive bacteria, Gram-negative bacteria and a yeast pathogen.The plot of log 1/MIC values ensures that the antimicrobial activity increases with the height of the plotted bars.
As results from the plotted data, the antimicrobial activity of the investigated gemini surfactants does not exceed the activity of the standard ciprofloxacin.The activity against Gram-positive and Gram-negative bacteria decreases moderately up to the m ≤ 14 and more abruptly as the alkyl chain is extended to 15 carbon atoms (AM15) for both pathogens.Similar results were found for the antimicrobial activity of aqueous solutions of a series of gemini surfactants with variable alkyl chain length m and a structure identical to AM(m) surfactants except for the presence of two ester groups instead of two amide groups in the spacer-the compounds No. IV, V and VI in the paper [68] (hereinafter referred to as EM(m) surfactants).For the sake of the comparison with the AM(m) gemini series, the MIC data from [68] are recalculated to log 1/MIC values and plotted in Fig. 9 with AM(m) series of identical or comparable alkyl chain length.
Several conclusions can be made from the comparison shown in Fig. 9.Both AM(m) and EM(m) series show a weaker activity against the yeast pathogen which is obvious for diester gemini surfactants EM(m).The differences in activity between AM(m) and EM(m) surfactants at the same alkyl length are not large.AM(m) surfactants are somewhat less efficient against Gram-positive bacteria than EM(m) gemini surfactants at the same alkyl length, while they perform better against Gram-negative pathogens than EM(m) diester surfactants.These differences, however, diminish with the increasing alkyl chain length at m = 15, 16.This indicates a poor interaction of long-chain homologs of AM(m) and EM(m) series with the cell wall of the studied pathogens.The presence of amide or ester groups in the surfactant's structure does not affect antimicrobial efficiency at this alkyl length.The antimicrobial effect is governed primarily by the interplay between the gemini surfactant solubility and the ability of a gemini molecule to incorporate itself into the surface layers of pathogen cells.This results in an optimum alkyl chain length of surfactant at which a maximum in biological activity vs alkyl chain length dependence, the so-called cut-off effect, is observed [69].The maximum antimicrobial activity of the EM(m) series was found at m = 12 (the EM(m) studies included shorter chain homologs starting from m = 8) [68].It allows us to predict that the found largest antimicrobial activity of AM12 would also represent the maximum value of antimicrobial efficiency against the investigated pathogens.

Conclusions
Critical micelle concentration values of AM(m) surfactants were found to be in the range 0.83 to 0.06 mM.They decrease with the increasing alkyl chain length from 12 to 15 carbon atoms.The interfacial area only weakly depends on the alkyl chain length.A more pronounced decrease in the interfacial area is observed for the longchain homolog AM15.The micelle ionisation degree increases with the increasing alkyl chain length, especially for long-chain homologs AM14 and AM15.The Gibbs free energy values per molecule and alkyl chain show a weak dependence on the alkyl chain length with the values − 67 to − 65 kJ/mol and − 35 to − 33 kJ/mol, respectively.The negative values indicate a spontaneous micellisation effect for the whole surfactant series.The particle size analysis shows that AM12 and AM13 form small spherical micelles with a size of approximately 6-7 nm while the hydrodynamic size of AM14` and AM15 increased to 137 nm and 169 nm, respectively.The zeta potential of AM(m) gemini surfactants shows an increase with m, from + 35 mV for AM12 up to + 83 mV for AM15.The aggregation number of AM(m) surfactants strongly depends on surfactant alkyl chain length.Short-chain gemini surfactants AM12 and AM13 have small aggregation numbers in the range 26-29.AM14 and AM15 show larger aggregation numbers while maintaining spherical or spheroidal shape of micelles.Antimicrobial activity against Gram-positive, Gram-negative bacteria, and the yeast increased with the decreasing number m of carbon The cut-off effect is proposed to explain the observed dependence on the alkyl chain length.

Fig. 1 Table 1 AM
Fig. 1 Dependence of surface tension on log surfactant concentration for AM12-AM15 gemini surfactants

Fig. 2
Fig. 2 Electrical conductivity vs. surfactant concentration plots for AM12-AM15 gemini surfactants Fig. 3 a cmc, b interfacial area A, c micellisation degree α, d Gibbs free energy per surfactant molecule ΔG molecule and alkyl chain ΔG chain plotted as a function of m

Fig. 4 aFig. 5
Fig. 4 a Hydrodynamic diameter d, b zeta potential of AM12-AM15 gemini surfactants plotted as a function of m at the surfactant concentration 10 × cmc

Fig. 6 a
Fig. 6 a Micelle aggregation number N plotted as a function of c/cmc for AM12-AM15 gemini surfactants as determined by time-resolved fluorescence quenching.b N plotted as a function of m for all investigated AM(m) surfactants at c/cmc = 10

Fig. 8 Fig. 9
Fig.8 Plot of log inverse minimum inhibitory concentration log (1/MIC) determined against Gram-positive bacteria, Gram-negative bacteria and a yeast pathogen for AM(m) surfactants

Table 2
Values of the fitting parameter R, micelle aggregation number N of gemini surfactants AM12-AM15, at the concentration 4 × cmc to 30 × cmc as determined from time-resolved fluorescence quenching measurements