The interactions and structure of secondary alcohol ethoxylates with 15 and 40 ethoxylate units in water near a calcite surface are studied. It is found that water binds preferentially to the calcite surface. Prediction of the free-energy landscape for surfactant molecules shows that single-surfactant molecules do not adsorb because they cannot get close enough to the surface because of the water layer for attractive ethoxylate-calcite or dispersion interactions to be significant. Micelles can adsorb onto the surface even with the intervening water layer because of the integrative effect of the attractive interactions of all the surfactant molecules. Adsorption is found to increase because of the closer proximity of the micelles to the surface due to a weakened water layer at higher temperatures. The free-energy well and barrier values are used to estimate surface to bulk partition coefficients for different surfactants and temperatures, and qualitative agreement is found with experimental observations. The combined effect of surfactant-water and surfactant-solid interactions is found to be responsible for an increased adsorption for nonionic surfactants as the system approaches the cloud point.